Acoustic double negativity induced by position correlations within a disordered set of monopolar resonators. Lanoy, M., J. H. Page, G. Lerosey, F. Lemoult, A. Tourin, and V. Leroy. Physical Review B 96, no. 22 (2017).
Résumé: © 2017 American Physical Society. Using a multiple scattering theory algorithm, we investigate numerically the transmission of ultrasonic waves through a disordered locally resonant metamaterial containing only monopolar resonators. By comparing the cases of a perfectly random medium with its pair correlated counterpart, we show that the introduction of short range correlation can substantially impact the effective parameters of the sample. We report, notably, the opening of an acoustic transparency window in the region of the hybridization band gap. Interestingly, the transparency window is found to be associated with negative values of both effective compressibility and density. Despite this feature being unexpected for a disordered medium of monopolar resonators, we show that it can be fully described analytically and that it gives rise to negative refraction of waves.


Acoustic monitoring of a ball sinking in vibrated granular sediments. Van Den Wildenberg, S., J. Léopoldès, A. Tourin, and X. Jia. In EPJ Web of Conferences. Vol. 140., 2017.
Résumé: © The Authors, published by EDP Sciences, 2017. We develop an ultrasound probing to investigate the dynamics of a high density ball sinking in 3D opaque dense granular suspensions under horizontal weak vibrations. We show that the motion of the ball in these horizontally vibrated glass bead packings saturated by water is consistent with the frictional rheology. The extracted stressstrain relation evidences an evolution of flow behaviour from frictional creep to inertial regimes. Our main finding is that weak external vibration primarily affects the yield stress and controls the depth of sinking via vibrationinduced sliding at the grain contact. Also, we observe that the extracted rheological parameters depend on the size of the probing ball, suggesting thus a nonlocal rheology.


Time reversal of ultrasound in granular media. Harazi, M., Y. Yang, M. Fink, A. Tourin, and X. Jia. European Physical Journal: Special Topics 226, no. 7 (2017): 1487–1497.
Résumé: © 2017, The Author(s).Time reversal (TR) focusing of ultrasound in granular packings is experimentally investigated. Pulsed elastic waves transmitted from a compressional or shear transducer source are measured by a TR mirror, reversed in time and backpropagated. We find that TR of ballistic coherent waves onto the source position is very robust regardless driving amplitude but provides poor spatial resolution. By contrast, the multiply scattered coda waves offer a finer TR focusing at small amplitude by a lens effect. However, at large amplitude, these TR focusing signals decrease significantly due to the vibrationinduced rearrangement of the contact networks, leading to the breakdown of TR invariance. Our observations reveal that granular acoustics is in between particle motion and wave propagation in terms of sensitivity to perturbations. These laboratory experiments are supported by numerical simulations of elastic wave propagation in disordered 2D percolation networks of masses and springs, and should be helpful for source location problems in natural processes.


Band gaps in bubble phononic crystals. Leroy, V., A. Bretagne, M. Lanoy, and A. Tourin. AIP Advances 6, no. 12 (2016).
Résumé: © 2016 Author(s).We investigate the interaction between Bragg and hybridization effects on the band gap properties of bubble phononic crystals. These latter consist of air cavities periodically arranged in an elastomer matrix and are fabricated using softlithography techniques. Their transmission properties are affected by Bragg effects due to the periodicity of the structure as well as hybridization between the propagating mode of the embedding medium and bubble resonance. The hybridization gap survives disorder while the Bragg gap requires a periodic distribution of bubbles. The distance between two bubble layers can be tuned to make the two gaps overlap or to create a transmission peak in the hybridization gap.


Sound velocity fluctuations in confined granular materials: Coarsegraining lengths and elastic heterogeneities. Van Den Wildenberg, S., A. Tourin, and X. Jia. Epl 115, no. 3 (2016).


Time reversal focusing and the diffraction limit. Fink, M., J. De Rosny, G. Lerosey, and A. Tourin. In Proceedings of the International School of Physics “Enrico Fermi”, 155–177. Vol. 173., 2011.
Résumé: Time reversal mirrors refocus an incidentwave field to the position of the original source, regardless of the complexity of the propagation medium. TRMs have now been implemented in a variety of physical scenarios from GHz Microwaves to MHz Ultrasonics and to hundreds of Hz in ocean acoustics. Common to this broad range of scales is a remarkable robustness exemplified by observations at all scales that the more complex the medium (random or chaotic), the sharper the focus. A TRM acts as an antenna that uses complex environments to appear wider than it is, resulting, for a broadband pulse, in a refocusing quality that does not depend on the TRM aperture. Moreover, when the complex environment is located in the near field of the source, time reversal focusing opens completely new approaches to superresolution. We will shown that, for a broadband source located inside a random metamaterial, a TRM located in the far field radiates a timereversed wave that interacts with the random medium to regenerate not only the propagating but also the evanescent waves required to refocus below the diffraction limit. © 2011 by Società Italiana di Fisica.


Manipulating bubbles with secondary Bjerknes forces. Lanoy, M., C. Derec, A. Tourin, and V. Leroy. Applied Physics Letters 107, no. 21 (2015).
Résumé: © 2015 AIP Publishing LLC. Gas bubbles in a sound field are submitted to a radiative force, known as the secondary Bjerknes force. We propose an original experimental setup that allows us to investigate in detail this force between two bubbles, as a function of the sonication frequency, as well as the bubbles radii and distance. We report the observation of both attractive and, more interestingly, repulsive Bjerknes force, when the two bubbles are driven in antiphase. Our experiments show the importance of taking multiple scatterings into account, which leads to a strong acoustic coupling of the bubbles when their radii are similar. Our setup demonstrates the accuracy of secondary Bjerknes forces for attracting or repealing a bubble, and could lead to new acoustic tools for noncontact manipulation in microfluidic devices.


Subwavelength focusing in bubbly media using broadband time reversal. Lanoy, M., R. Pierrat, F. Lemoult, M. Fink, V. Leroy, and A. Tourin. Physical Review B 91, no. 22 (2015).


Superabsorption of acoustic waves with bubble metascreens. Leroy, V., A. Strybulevych, M. Lanoy, F. Lemoult, A. Tourin, and J. H. Page. Physical Review B 91 (2015): 020301.
Résumé: A bubble metascreen, i.e., a single layer of gas inclusions in a soft solid, can be modeled as an acoustic open resonator, whose behavior is well captured by a simple analytical expression. We show that by tuning the parameters of the metascreen, acoustic superabsorption can be achieved over a broad frequency range, which is confirmed by finite element simulations and experiments. Bubble metascreens can thus be used as ultrathin coatings for turning acoustic reflectors into perfect absorbers.


Transverse localization of sound. Bretagne, A., M. Fink, and A. Tourin. Physical Review B – Condensed Matter and Materials Physics 88, no. 10 (2013).
Résumé: We show how disorder can be used to guide a broadband ultrasonic wave. The idea is to exploit the transverse localization regime that has been reported for light. Our waveguide consists of a set of parallel cylindrical scatterers randomly distributed in the transverse plane. An ultrasonic beam propagating along the direction of scatterers is found to remain confined in the two other directions on a size smaller than the waveguide diameter and driven by the localization length. Interestingly, the guided wave is also found to propagate with a very limited temporal dispersion. © 2013 American Physical Society.


Optimal spatiotemporal focusing through complex scattering media. Aulbach, J., A. Bretagne, M. Fink, M. Tanter, and A. Tourin. In 2012 Conference on Lasers and ElectroOptics, CLEO 2012., 2012.
Résumé: We demonstrate, based on spatial and frequency resolved wave front shaping of ultrasound with a nonlinear feedback signal, how to achieve optimal spatiotemporal focusing through a complex scattering medium. © 2012 OSA.
MotsClés: Scattering media; Scattering medium; Spatiotemporal focusing; Wave front shaping; Lasers; Optimization


Compact MIMO antenna arrays using metamaterial hybridization band gaps. Lerosey, G., C. Leray, F. Lemoult, J. De Rosny, and A. Tourin. In IEEE Antennas and Propagation Society, APS International Symposium (Digest), 774–777., 2012.
Résumé: In this talk, we show how the concept of hybridization band gap in metamaterials can be utilized to create antennas for MIMO applications. Those strongly decoupled antennas present at the same time a very small form factor and a very low correlation. To that aim, we first explain briefly the concept of hybridization between a resonator and the free space waves continuum. Then we expose the methodology we use to design multiports antennas based on that concept. We present results of several antennas designed using this idea, especially in the wifi bands, and give potential solutions for multiband compact MIMO antennas for LTE applications. © 2012 IEICE.
MotsClés: Free spaces; Low correlation; MIMO antenna; MIMO applications; Multiband; Potential solutions; Small form factors; Antenna arrays; Approximation theory; Energy gap; Metamaterials; Metamaterial antennas


Hybridization band gap based smart antennas: Deep subwavelength yet directional and strongly decoupled MIMO antennas. Lerosey, G., C. Leray, F. Lemoult, J. De Rosny, A. Tourin, and M. Fink. In Proceedings of 6th European Conference on Antennas and Propagation, EuCAP 2012, 2697–2701., 2012.
Résumé: In this paper, we show how the concept of hybridization band gaps can be utilized to create antennas for MIMO applications. Those strongly decoupled antennas present at the same time a very small form factor and a very low correlation. To that aim, we first explain briefly the concept of hybridization between a resonator and the free space waves continuum. Then we expose the methodology we use to design multiports antennas based on that concept. We present numerical and experimental results of 2 ports MIMO antennas at 2.45 GHz, printed on a PCB, whose areas are smaller than 2.6*2.6 cm 2. The two ports display experimentally peak gains of a about 4 dB, efficiencies of 80%, a coupling lower than 30 dB and a correlation lower than 0.1. © 2012 IEEE.
MotsClés: compact antenna arrays; electromagnetic band gap antennas; metamaterials; MIMO antennas; photonic crystals; Smart antennas; Compact antenna; Electromagnetic band gap antennas; Free spaces; Low correlation; MIMO antenna; MIMO applications; Peak gain; Small form factors; Subwavelength; Approximation theory; Energy gap; Metamaterials; Photonic crystals; Smart antennas; Metamaterial antennas


Bragg and hybridization gaps in bubble phononic crystals. Bretagne, A., B. Venzac, V. Leroy, and A. Tourin. In AIP Conference Proceedings, 317–318. Vol. 1433., 2012.
Résumé: We experimentally investigate the existence of Bragg and hybridization gaps in 3D bubble phononic crystals. Softlithography techniques allow us to tune the lattice constant, so that we can highlight the interactions between the two types of gaps. We show that a layered model provides a simple physical picture of the phenomenon. © 2012 American Institute of Physics.
MotsClés: Band gap; hybridization; lowfrequency resonance; Phononic crystal


Imaging changes in scattering media from Time Reversal of the Coda wave Difference (TRECOD). Bonneau, L., C. Prada, M. Fink, and A. Tourin. Waves in Random and Complex Media 22, no. 1 (2012): 109–120.
Résumé: We propose a new method for monitoring temporal changes in a complex scattering environment. It is referred to as Time Reversal of the Coda wave Difference (TRECOD). The impulse responses of the probed medium are recorded between all the emitter/receiver pairs of a transceiver array. A Fourier transform of these responses then produces the socalled backscattering transfer matrix at each frequency of the transceiver bandwidth. The matrix acquisition is repeated and the image of the temporal changes occurring between two matrix acquisitions is formed by propagating numerically the significant singular vectors of the matrix difference. Smallscale experiments with ultrasound are used to validate the method and demonstrate its interest for the monitoring of a fluid injection in a porous medium behind a strongly scattering obstacle. © 2012 Copyright Taylor and Francis Group, LLC.
MotsClés: Coda waves; Fluid injections; matrix; Porous medium; Scattering environment; Scattering media; Singular vectors; Smallscale experiment; Temporal change; Time reversal; Transceiver array; Transfer matrixes; Porous materials; Transceivers; Transfer matrix method; Scattering


Optimal spatiotemporal focusing through complex scattering media. Aulbach, J., A. Bretagne, M. Fink, M. Tanter, and A. Tourin. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 85, no. 1 (2012).
Résumé: We present an alternative approach for spatiotemporal focusing through complex scattering media by wave front shaping. Using a nonlinear feedback signal to shape the incident pulsed wave front, we show that the limit of a spatiotemporal matched filter can be achieved; i.e., the wave amplitude at the intended time and focus position is maximized for a given input energy. It is exactly what is also achieved with time reversal. Demonstrated with ultrasound experiments, our method is generally applicable to all types of waves. © 2012 American Physical Society.
MotsClés: Alternative approach; Focus positions; Input energy; Pulsed wave; Scattering media; Spatiotemporal focusing; Time reversal; Wave amplitudes; Wave front shaping; Condensed matter physics; Physics; Wavefronts


R&D program for French sodium fast reactor: On the description and detection of sodium boiling phenomena during subassembly blockages. Vanderhaegen, M., K. Paumel, J. M. Seiler, A. Tourin, J. P. Jeannot, and G. Rodriguez. In ANIMMA 2011 – Proceedings: 2nd International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and their Applications., 2011.
Résumé: In support of the French ASTRID (Advanced Sodium Technological Reactor for Industrial Demonstration) reactor program, which aims to demonstrate the industrial applicability of sodium fast reactors with an increased level of safety demonstration and availability compared to the past French sodium fast reactors, emphasis is placed on reactor instrumentation. It is in this framework that CEA studies continuous core monitoring to detect as early as possible the onset of sodium boiling. Such a detection system is of particular interest due to the rapid progress and the consequences of a Total Instantaneous Blockage (TIB) at a subassembly inlet, where sodium boiling intervenes in an early phase. In this paper, the authors describe all the particularities which intervene during the different boiling stages and explore possibilities for their detection. © 2011 IEEE.
MotsClés: Acoustic Detection; Boiling; Sodium; Acoustic detection; Boiling stage; Detection system; Level of safeties; Reactor instrumentation; Reactor program; Sodium boiling; Subassembly; Boiling liquids; Fast reactors; Liquid metal cooled reactors; Nuclear instrumentation; Phase transitions; Sodium


Enhanced and reduced transmission of acoustic waves with bubble metascreens. Bretagne, A., A. Tourin, and V. Leroy. Applied Physics Letters 99, no. 22 (2011).
Résumé: We present a class of sonic metascreens for manipulating airborne acoustic waves at ultrasonic or audible frequencies. Our screens consist of periodic arrangements of air bubbles in water or possibly embedded in a soft elastic matrix. They can be used for soundproofing but also for exalting transmission at an air/water interface or even to achieve enhanced absorption. © 2011 American Institute of Physics.
MotsClés: Air bubbles; Air/Water Interfaces; Audible frequency; Elastic matrix; Enhanced absorption; Acoustic waves; Acoustics


Time reversal in subwavelengthscaled resonant media: Beating the diffraction limit. Lemoult, F., A. Ourir, J. De Rosny, A. Tourin, M. Fink, and G. Lerosey. International Journal of Microwave Science and Technology (2011).
Résumé: Time reversal is a physical concept that can focus waves both spatially and temporally regardless of the complexity of the propagation medium. Time reversal mirrors have been demonstrated first in acoustics, then with electromagnetic waves, and are being intensively studied in many fields ranging from underwater communications to sensing. In this paper, we will review the principles of time reversal and in particular its ability to focus waves in complex media. We will show that this focusing effect depends on the complexity of the propagation medium rather than on the time reversal mirror itself. A modal approach will be utilized to explain the physical mechanism underlying the concept. A particular focus will be given on the possibility to break the diffraction barrier from the far field using time reversal. We will show that finite size media made out of coupled subwavelength resonators support modes which can radiate efficiently in the far field spatial information of the near field of a source. We will show through various examples that such a process, due to reversibility, permits to beat the diffraction limit using far field time reversal, and especially that this result occurs owing to the broadband inherent nature of time reversal. © 2011 Fabrice Lemoult et al.


Experimental validation of time reversal ultra wideband communication system for high data rates. Naqvi, I. H., G. E. Zein, G. Lerosey, J. De Rosny, P. Besnier, A. Tourin, and M. Fink. IET Microwaves, Antennas and Propagation 4, no. 5 (2010): 643–650.
Résumé: An experimental validation of high data rate communication for a time reversal (TR) ultra wideband (UWB) communication system is performed using binary pulse amplitude modulation (BPAM) in two different dense multipath propagation channels for different data rates (15.62Mbps≤Rb≤1Gbps). From the measured received signals, signal, interference and noise contributions are separated. At very high data rates, interference has the most dominant contribution of all. Furthermore, without any processing and equalisation at the receiver, bit error rate (BER) performance is compared for different Rb It is shown that for Rb≤125Mbps, TR system gives a good BER performance. Finally, the authors introduce a modified TR scheme in which total bandwidth of the TR system is divided into Nsubbands contributing equal power in the power spectral density (PSD). This technique enables a flat PSD of the TR transmitted signal, reduces inter symbol interference (ISI) and therefore improves the BER performance of the system. © 2010 © The Institution of Engineering and Technology.
MotsClés: BER performance; Bit error rate performance; Data rates; Dense multipath; Dominant contributions; Equalisation; Experimental validations; High data rate; High data rate communications; Noise contributions; Propagation channels; Received signals; Time reversal; Transmitted signal; Ultrawideband communications; Amplitude modulation; Broadband networks; Communication systems; Data flow analysis; Power spectral density; Pulse amplitude modulation; Satellite communication systems; Bit error rate


Design and characterization of bubble phononic crystals. Leroy, V., A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin. Applied Physics Letters 95, no. 17 (2009).
Résumé: We report the practical realization of phononic crystals with gas inclusions, using soft lithography techniques. Ultrasonic experiments from 0.3 to 5 MHz confirm the existence of deep and wide minima of transmission through the crystal. We show that the first gap is due to the combined effects of Bragg reflections and bubble resonances. We propose a simple layered model that gives a reasonable prediction of the ultrasonic transmission. © 2009 American Institute of Physics.
MotsClés: Bragg reflection; Combined effect; Gas inclusions; Layered model; Phononic Crystal; Practical realizations; Soft lithography; Ultrasonic experiments; Phonons; Ultrasonics; Crystals


Timereversed waves and superresolution. Fink, M., J. de Rosny, G. Lerosey, and A. Tourin. Comptes Rendus Physique 10, no. 5 (2009): 447–463.
Résumé: Timereversal mirrors (TRMs) refocus an incident wavefield to the position of the original source regardless of the complexity of the propagation medium. TRMs have now been implemented in a variety of physical scenarios from GHz microwaves to MHz ultrasonics and to hundreds of Hz in ocean acoustics. Common to this broad range of scales is a remarkable robustness exemplified by observations at all scales that the more complex the medium (random or chaotic), the sharper the focus. A TRM acts as an antenna that uses complex environments to appear wider than it is, resulting for a broadband pulse, in a refocusing quality that does not depend on the TRM aperture. Moreover, when the complex environment is located in the near field of the source, timereversal focusing opens completely new approaches to superresolution. We will show that, for a broadband source located inside a random metamaterial, a TRM located in the far field radiated a timereversed wave that interacts with the random medium to regenerate not only the propagating but also the evanescent waves required to refocus below the diffraction limit. This focusing process is very different from that developed with superlenses made of negative index material only valid for narrowband signals. We will emphasize the role of the frequency diversity in timereversal focusing. To cite this article: M. Fink et al., C. R. Physique 10 (2009). © 2009.
MotsClés: Metamaterials; Timereversal mirror


Eigenvalue distributions of correlated multichannel transfer matrices in strongly scattering systems. Sprik, R., A. Tourin, J. De Rosny, and M. Fink. Physical Review B – Condensed Matter and Materials Physics 78, no. 1 (2008).
Résumé: We experimentally study the effects of correlations in the propagation of ultrasonic waves in water from a multielement source to a multielement detector through a strongly scattering system of randomly placed vertical rods. Due to the strong scattering, the wave transport in the sample is in the diffusive regime. The correlation between the waves is induced when the distance between transducer elements is within the coherence region of the scattered sound. We measure the multichannel transfer matrix H, each element of which represents the signal strength between the m individual transmitters and n receivers. The observed eigenvalue distribution of the matrix H H† clearly shows the effect of correlations between channels and can be interpreted using random matrix theory. These results are of practical importance in many areas, e.g., for evaluating the information transfer capacity of such a complex scattering system. © 2008 The American Physical Society.


Focusing beyond the diffraction limit with farfield time reversal. Lerosey, G., J. De Rosny, A. Tourin, and M. Fink. Science 315, no. 5815 (2007): 1120–1122.
Résumé: We present an approach for subwavelength focusing of microwaves using both a timereversal mirror placed in the far field and a random distribution of scatterers placed in the near field of the focusing point. The farfield timereversal mirror is used to build the timereversed wave field, which interacts with the random medium to regenerate not only the propagating waves but also the evanescent waves required to refocus below the diffraction limit. Focal spots as small as onethirtieth of a wavelength are described. We present one example of an application to telecommunications, which shows enhancement of the information transmission rate by a factor of 3.
MotsClés: diffraction; microwave radiation; telecommunication; wavelength; acoustics; article; diffraction; lens; lithotripsy; microwave radiation; priority journal; scanning near field optical microscopy; sound transmission; technology; telecommunication; time; ultrasound


Coherent backscattering and farfield beamforming in acoustics. Aubry, A., A. Derode, P. Roux, and A. Tourin. Journal of the Acoustical Society of America 121, no. 1 (2007): 70–77.
Résumé: Coherent backscattering of waves by a random medium is spectacular evidence of interference effects despite disorder and multiple scattering. It manifests itself as a doubling of the wave intensity reflected exactly in the backward direction. This phenomenon has been observed experimentally in optics, acoustics, or seismology. While optical measurements are realized in farfield conditions with a plane wave illumination and a beamwidth much larger than the wavelength, ultrasonic experiments are carried out with wideband controllable arrays of (nearly) pointlike transducers that directly record the wave field, in amplitude and phase. Therefore it is possible to perform beamforming of the incoming and outgoing wave fields before computing the average backscattered intensity. In this paper, the advantages of plane wave beamforming applied to the study of the coherent backscattering effect are shown. Particularly, the angular resolution, the signaltonoise ratio, as well as the estimation of the enhancement factor can be improved by beamforming. Experimental results are presented with ultrasonic pulses, in the 2.53.5 MHz range, propagating in random collections of scatterers. Since the coherent backscattering effect can be taken advantage of to measure diffusive parameters (transport mean free path, diffusion constant), planewave beamforming can be applied to the characterization of highly scattering media. © 2007 Acoustical Society of America.
MotsClés: Signal interference; Signal to noise ratio; Transducers; Ultrasonics; Beamforming; Coherent backscattering effects; Plane wave beamforming; Acoustic wave backscattering; acoustics; article; beamforming; coherent backscattering; measurement; priority journal; signal noise ratio; transducer


Timereversal imaging of seismic sources and application to the great Sumatra earthquake. Larmat, C., J.  P. Montagner, M. Fink, Y. Capdeville, A. Tourin, and E. Clévédé. Geophysical Research Letters 33, no. 19 (2006).
Résumé: The increasing power of computers and numerical methods (like spectral element methods) allows continuously improving modelization of the propagation of seismic waves in heterogeneous media and the development of new applications in particular time reversal in the threedimensional Earth. The concept of timereversal (hereafter referred to as TR) was previously successfully applied for acoustic waves in many fields like medical imaging, underwater acoustics and non destructive testing. We present here the first application at the global scale of TR with associated reverse movies of seismic waves propagation by sending back long period timereversed seismograms. We show that seismic wave energy is refocused at the right location and the right time of the earthquake. When TR is applied to the SumatraAndaman earthquake (26 Dec. 2004), the migration of the rupture from the south towards the north is retrieved. Therefore, TR is potentially interesting for constraining the spatiotemporal history of complex earthquakes. Copyright 2006 by the American Geophysical Union.
MotsClés: Acoustic waves; Earth (planet); Earthquakes; Nondestructive examination; Seismic waves; Underwater acoustics; Reverse movies; Sumatra earthquake; Timereversal imaging; Seismic prospecting; acoustic wave; earthquake rupture; heterogeneous medium; imaging method; numerical model; seismic source; seismic wave; seismogram; Sumatra earthquake 2004; wave energy; wave propagation


Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium. Derode, A., V. Mamou, and A. Tourin. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 74, no. 3 (2006).
Résumé: Experimental measurements of the coherent wave transmission for ultrasonic waves propagating in water through a random set of scatterers (metallic rods) are presented. Though the densities are moderate (6% and 14%) the experimental results show that the meanfree path deviates from the classical firstorder approximation due to the existence of correlations between scatterers. Theoretical results for the mean free path obtained from different approaches are compared to the experimental measurements. The best agreement is obtained with the secondorder diagrammatic expansion of the selfenergy. © 2006 The American Physical Society.
MotsClés: Approximation theory; Electromagnetic wave propagation; Optical correlation; Random processes; Ultrasonic waves; Coherent waves; Diagrammatic expansion; Random medium; Ultrasonic wave propagation; Coherent light


Time reversal telecommunications in complex environments. Tourin, A., G. Lerosey, J. de Rosny, A. Derode, and M. Fink. Comptes Rendus Physique 7, no. 7 (2006): 816–822.
Résumé: The time reversal technique is well known in acoustics and has lead to remarkable applications in ultrasound and underwater acoustics. Here we propose to apply it to MIMO (Multiple Input – Multiple Output) UWB (Ultra Wide Band) communication: in a first 'training' step, the intended user transmits an electromagnetic pulse that propagates in a medium, where it undergoes multiple reflections. The resulting signals are recorded at the base station by one or more antennas, time reversed and used to precode the transmitted symbols. The resulting sequences are sent back by the antennas. The timereversed wave retraces its former paths and leads to a focus of the message in space and time at the receiver. The equalization step is thus simplified since TR compensates for the reverberation caused by the channel. Furthermore, TR takes advantage of the multipaths to increase the signal strength at the receiver and to improve spatial focusing. To cite this article: A. Tourin et al., C. R. Physique 7 (2006). © 2006 Académie des sciences.
MotsClés: MIMO; Multiple scattering; Reverberation; Time reversal; UWB


Time reversal of wideband microwaves. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, and M. Fink. Applied Physics Letters 88, no. 15 (2006).
Résumé: In this letter, time reversal is applied to wideband electromagnetic waves in a reverberant room. To that end a multiantenna time reversal mirror (TRM) has been built. A 150 MHz bandwidth pulse at a central frequency of 2.45 GHz is radiated by a monopolar antenna, spread in time due to reverberation, recorded at the TRM, time reversed, and retransmitted. The timereversed wave converges back to its source and focus in both time and space. The time compression is studied versus the number of antennas in the TRM and its bandwidth. The focal spot is also measured thanks to an eightchannel receiving array. © 2006 American Institute of Physics.
MotsClés: Arrays; Bandwidth; Microwave antennas; Mirrors; Reverberation; Monopolar antenna; Receiving array; Time reversal mirror (TRM); Microwaves


Time reversal of ultrasound through a phononic crystal. Tourin, A., F. Van Der Biest, and M. Fink. Physical Review Letters 96, no. 10 (2006).
Résumé: In this Letter, we experimentally investigate time reversal focusing through a phononic crystal consisting of a periodic square arrangement of steel rods in water. An acoustic pulse is transmitted through the medium, received at a transducer array, time reversed and backpropagated. Both spatial focusing and time compression are studied and compared with those obtained through an equivalent disordered medium. With the phononic crystal, we do not observe the “hyperfocusing effect” that is typical of time reversal through disordered samples. © 2006 The American Physical Society.
MotsClés: Phononic crystals; Steel rods; Transducer array; Backpropagation; Photons; Steel; Transducers; Crystalline materials


Time reversal of electromagnetic waves and telecommunication. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink. Radio Science 40, no. 6 (2005).
Résumé: [1] Time reversal (TR) communication in various configurations (single input, single output (SISO); multiple inputs, single output (MISO); or multiple inputs, multiple outputs (MIMO)) is studied. In particular, we report an experimental demonstration of time reversal focusing with electromagnetic waves in a SISO scheme. An antenna transmits a 1 μs electromagnetic pulse at a central frequency of 2.45 GHz in a highQ cavity. Another antenna records the strongly reverberated signal. The timereversed wave is built and transmitted back by the same antenna acting now as a time reversal mirror. The wave is found to converge to its initial source and is compressed in time. The quality of focusing is determined by the frequency bandwidth and the spectral correlations of the field within the cavity. A spatial focusing of the compressed pulse is also shown. This experiment is the first step for a communication scheme based on time reversal. It would be very interesting for ultrawideband communication in complex media since TR would permit compensation for delay spreading. MISO and MIMO TR communications are discussed on the basis of smallscale experiments with ultrasound. In particular, the binary error rate of the method is studied as a function of both data rate and external noise. A simple theoretical approach explains the results. Copyright 2005 by the American Geophysical Union.
MotsClés: Antennas; Bandwidth; Error analysis; Functions; Telecommunication systems; Binary error rate; Complex media; Ultrawideband communication; Electromagnetic waves


Weak localization and time reversal of ultrasound in a rotational flow. De Rosny, J., A. Tourin, A. Derode, P. Roux, and M. Fink. Physical Review Letters 95, no. 7 (2005).
Résumé: A onechannel timereversal (TR) experiment is performed inside a rough reverberating cavity in the presence of a rotational flow. The amplitude of the TR wave is plotted versus the distance between the TR channel and the initial source: when they coincide, it exhibits a “timereversal enhancement” (TRE). With no flow, the TRE is the same as the coherent backscattering enhancement (CBE). But contrary to CBE, the TRE peak is shown to be insensitive to the breaking down of reciprocity due to the flow. This new effect of weak localization is sustained by a diagrammatic approach. © 2005 The American Physical Society.
MotsClés: Coherent backscattering enhancement (CBE); Weak localization; Backscattering; Coherent light; Light sources; Rotational flow; Ultrasonics


Resonant tunneling of acoustic waves through a double barrier consisting of two phononic crystals. Van Der Biest, F., A. Sukhovich, A. Tourin, J. H. Page, B. A. Van Tiggelen, Z. Liu, and M. Fink. Europhysics Letters 71, no. 1 (2005): 63–69.
Résumé: We present the acoustic analog of resonant tunneling through a double barrier in quantum mechanics. Pairs of identical phononic crystals, in both 2D and 3D, were assembled and separated by a uniform spacer, forming a resonant cavity. The ultrasonic transmission exhibits resonant peaks at frequencies inside the band gaps, where ultrasound tunneling through each phononic crystal occurs. On resonance, the measured group time is large and even predicted to increase exponentially with the thickness of the crystals in the absence of absorption, while off resonance very fast speeds are found. © EDP Sciences.


Phononic crystals. Page, J. H., A. Sukhovich, S. Yang, M. L. Cowan, F. Van Der Biest, A. Tourin, M. Fink, Z. Liu, C. T. Chan, and P. Sheng. Physica Status Solidi (B) Basic Research 241, no. 15 (2004): 3454–3462.
Résumé: Phononic crystals are periodic composite materials with lattice spacings comparable to the acoustic wavelength. They are of interest not only because of the profound effects of their periodic structure on wave propagation (e.g., the existence of acoustic band gaps), but also because of potential applications (e.g., their possible role in sound filters, transducer design and acoustic mirrors). In this paper, we summarize recent progress using ultrasonic experiments to investigate both two and threedimensional phononic crystals. By measuring the ultrasonic wave field transmitted through slabshaped samples of different thicknesses, both the dispersion curves and amplitude transmission coefficient can be determined. Because the field is pulsed, the dynamics of the wave fields can also be investigated; this has allowed us to make a systematic study of ultrasonic wave tunneling in phononic crystals. New results on resonant tunneling, focussing and negative refraction phenomena in phononic crystals are also presented. Our data are well explained using Multiple Scattering Theory, giving additional insight into the physical properties and potential applications of these novel materials. © 2004 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim.


Relation between time reversal focusing and coherent backscattering in multiple scattering media: A diagrammatic approach. De Rosny, J., A. Tourin, A. Derode, B. Van Tiggelen, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 70, no. 4 2 (2004): 04660104660112.
Résumé: Onechannel time reversal (TR) experiments through multiple scattering media were discussed. The hyperresolution and the selfaveraging property was described. It was found that the developed formalism leads to a deeper understanding of the role of the ladder and mostcrossed diagrams in a TR experiment. Results show that when the initial source and the time reversal point are at the same location, the timereversed amplitude is twice higher.
MotsClés: Approximation theory; Diffusion; Green's function; Mathematical models; Random processes; Spectroscopy; Statistical methods; Ultrasonic propagation; Paraxial approximation; Spatial focusing; Spatiotemporal focusing; Time reversal (TR); Acoustic wave backscattering


Telecommunication in a disordered environment with iterative time reversal. Montaldo, G., G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink. Waves Random Media 14, no. 3 (2004): 287–302.
Résumé: We present a method to transmit digital information through a highly scattering medium in a MIMOMU (multiple input multiple output multiple users) context. It is based on iterations of a timereversal process, and permits us to focus short pulses, both spatially and temporally, from a base antenna to different users. This iterative technique is shown to be more efficient (lower intersymbol interference and lower error rate) than classical timereversal communication, while being computationally light and stable. Experiments are presented: digital information is conveyed from 15 transmitters to 15 receivers by ultrasonic waves propagating through a highly scattering slab. From a theoretical point of view, the iterative technique achieves the inverse filter of propagation in the subspace of nonnull singular values of the timereversal operator. We also investigate the influence of external additive noise, and show that the number of iterations can be optimized to give the lowest error rate. © 2004 IOP Publishing Ltd.
MotsClés: Antenna lobes; Antennas; Digital communication systems; Eigenvalues and eigenfunctions; Iterative methods; Matrix algebra; Signal receivers; Transmitters; Ultrasonic propagation; Multiple input multiple output multiple users; Short pulses; Time reversal method; Electromagnetic wave scattering


Time reversal of electromagnetic waves. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink. Physical Review Letters 92, no. 19 (2004): 193904–1.
Résumé: A onechannel electromagnetic timereversal mirror (TRM) was used for investigating the feasibility of time reversal focusing with electromagnetic waves in the GHz range. Two omnidirectional antennas with a frequency of 2.45 GHz and two transceiver circuit boards were also used for the investigations. The baseband signals were time reversed and the wave carriers were phase conjugated in order to avoid digitizing the radio signals at GHz frequencies. The circuit boards demodulated the radio frequency signal back to the baseband. The frequency bandwidth and the spectral correlations determined the quality of focusing.
MotsClés: Analog to digital conversion; Bandwidth; Correlation methods; Demodulation; Light scattering; Light transmission; Low pass filters; Mirrors; Monochromators; Signal receivers; Signal to noise ratio; Transceivers; Ultrasonic effects; Wireless telecommunication systems; Phase conjugation; Quasimonochromatic signals; Spectral correlations; Time reversal mirrors (TRM); Antenna radiation


Taking advantage of multiple scattering to communicate with timereversal antennas. Derode, A., A. Tourin, J. De Rosny, M. Tanter, S. Yon, and M. Fink. Physical Review Letters 90, no. 1 (2003): 014301/1–014301/4.
Résumé: An overview is given of the experimental demonstration that highorder scattering in a disordered medium can help by increasing the information transfer rate, especially if the timereversal technique is used to naturally focus the different bistreams onto the receivers. The first key parameter in the experiment is the number of independent focal spots that can be created by the transmitting array in the receiving plane. The second key parameter is the number of uncorrelated frequencies within the bandwidth, which governs the peaktonoise ratio on each receiver.
MotsClés: Antenna arrays; Communication channels (information theory); Data communication systems; Decoding; Eigenvalues and eigenfunctions; Electromagnetic wave propagation; Fourier transforms; Matrix algebra; Signal receivers; Ultrasonic devices; Vectors; Wireless telecommunication systems; Time reversal antennas; Ultrasonic antennas; Electromagnetic wave scattering


Time reversal versus phase conjugation in a multiple scattering environment. Derode, A., A. Tourin, and M. Fink. Ultrasonics 40, no. 18 (2002): 275–280.
Résumé: We present experimental results on the reversibility of ultrasound in a multiple scattering medium. An ultrasonic pulsed wave is transmitted from a point source to a 128element receiving array through 2D samples with various thickness. The samples consist of random collections of parallel steel rods immersed in water. The scattered waves are recorded, time reversed and sent back into the medium. The timereversed waves are converging back to their source and the quality of spatial and temporal focusing on the source is related to the secondorder moments of the scattered wave (correlation) in time and in space. Experimental results show that it is possible to obtain a robust estimation of the correlations on a single realisation of disorder, taking advantage of the wide frequency bandwidth. The spatial resolution of the system is only limited by the correlation length of the scattered field, and no longer by diffraction. Moreover, successful timereversal focusing using a single element instead of an array is possible, whereas a onechannel monochromatic phase conjugation fails. The efficiency of broadband time reversal compared to monochromatic phase conjugation lies in the number of 'information grains' in the frequency bandwidth. © 2002 Elsevier Science B.V. All rights reserved.
MotsClés: Multiple scattering; Phase conjugation; Time reversal; Bandwidth; Focusing; Monochromators; Natural frequencies; Optical correlation; Optical phase conjugation; Optical resolving power; Robustness (control systems); Ultrasonic waves; Multiple scattering; Ultrasonic scattering


Sensitivity to perturbations of a timereversed acoustic wave in a multiple scattering medium. Tourin, A., A. Derode, and M. Fink. Physical Review Letters 87, no. 27 I (2001): 2743011–2743014.
Résumé: Analysis of experimental results on the robustness of acoustic focusing in a multiple scattering medium undergoing perturbations was presented. A time reversal experiment was performed to follow its timedependent evolution in a perturbed random medium. The method was found to be analogous to the diffusive acoustic wave spectroscopy developed to study fluidized suspensions of particles.
MotsClés: Optical correlation; Perturbation techniques; Scattering; Sensitivity analysis; Spectroscopic analysis; Transducers; Diffusive wave spectroscopy; Multiple scattering; Ultrasonic waves


Observation of a coherent backscattering effect with a dipolar source for elastic waves: Highlight of the role played by the source. De Rosny, J., A. Tourin, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 64, no. 6 II (2001): 066604/1–066604/4.
Résumé: Experimental evidence of the role played by the source on the coherent backscattering effect (CBE) for elastic waves was established. It was shown that using a dipolar source and a monopolar receiver, a “bicone” can be obtained instead of a simple cone that is well explained by describing dipolar as the superposition of two monopolar sources opposite in phases.
MotsClés: Aluminum; Computational methods; Eigenvalues and eigenfunctions; Elastic waves; Fourier transforms; Interferometers; Lenses; Modal analysis; Optical beam splitters; Silicon; Transducers; Bicone; Chaotic cavity; Coherent backscattering effect; Heterodyne interferometer; Multipolar emitterreceiver; Pointlike dipolar source; Silicon plate; Backscattering


Numerical and experimental timereversal of acoustic waves in random media. Derode, A., M. Tanter, A. Tourin, L. Sandrin, and M. Fink. Journal of Computational Acoustics 9, no. 3 (2001): 993–1003.
Résumé: In classical mechanics, a timereversal experiment with a large number of particles is impossible. Because of the high sensitivity to initial conditions, one would need to resolve the positions and velocities of each particle with infinite accuracy. Thus, it would require an infinite amount of information, which is of course out of reach. In wave physics however, the amount of information required to describe a wave field is limited and depends on the shortest wavelength of the field. Thus we can propose an acoustic equivalent of the experiment we mentioned above. We start with a coherent transient pulse, let it propagate through a disordered highly scattering medium, then record the scattered field and timereverse it: surprisingly, it travels back to its initial source, which is not predictable by usual theories for random media. Indeed, to study waves propagation in disordered media theoreticians, who find it difficult to deal with one realization of disorder, use concepts defined as an average over the realizations, which naturally leads to the diffusion approximation. But the corresponding equation is not timereversal invariant and thus fails in describing our experiment. Then, to understand our experimental results and try to predict new ones, we have developed a finite elements simulation based on the real microscopic timeinvariant equation of propagation. The experimental and numerical results are found to be in very good agreement.


Random multiple scattering of ultrasound. II. Is time reversal a selfaveraging process? Derode, A., A. Tourin, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 64, no. 3 II (2001): 366061–366113.
Résumé: The statistical moments of ultrasonic waves transmitted through a disordered medium with resonant multiple scattering were investigated. An ultrasonic pulsed wave was transmitted from a point source to a 128element receiving array through twodimensional samples with various thickness. The results show that a robust estimation on a single realization of disorder is obtained using wide frequency bandwidth.
MotsClés: Acoustic wave propagation; Backscattering; Bandwidth; Integral equations; Interfaces (computer); Mathematical models; Piezoelectric devices; Steel; Ultrasonic scattering; Ultrasonic pulsed waves; Ultrasonic waves


Random multiple scattering of ultrasound. I. Coherent and ballistic waves. Derode, A., A. Tourin, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 64, no. 3 II (2001): 366051–366057.
Résumé: Random multiple scattering of ultrasound was analyzed using statistical approach techniques. An ultrasonic pulsed wave transmitted from a point source to a 128element receiving array was studied through two dimensional samples with various thickness. It is found that the transmitted wave forms exhibits a timedependent frequency spectrum. The results show that the secondary wave forms on the coherent wave form is produced due to the presence of elastic resonance in the given frequency bandwidth.
MotsClés: Backscattering; Ballistics; Coherent light; Integral equations; Mathematical models; Ultrasonic scattering; Ballistic waves; Resonant multiple scattering; Ultrasonic waves


Multiple scattering of sound. Tourin, A., M. Fink, and A. Derode. Waves Random Media 10, no. 4 (2000): R31–R60.
Résumé: We present a topical review which summarizes the main contributions to `multiple scattering of acoustic and elastic waves' including the most recent advances.The review is divided into five main parts.In the first part, the effects of multiple scattering on ultrasonic propagation are illustrated on the basis of three experimental examples.In the second and third parts, we present the two possible descriptions for the propagation of an acoustic wave in a random medium. The first one is based on the study of the coherent wave, i.e. the wave amplitude averaged over disorder, whereas the second one deals with the propagation of the incoherent intensity, i.e. the intensity averaged over disorder. We especially insist on the microscopic basis for the phenomenological radiative transfer equation and show how it can be solved in the diffusion approximation. The theory is illustrated with experimental results obtained on a twodimensional multiplescattering prototype made of thousands of steel rods randomly distributed and immersed in water. In the fourth part, we present experimental evidence that the diffusion equation fails in describing all the aspects of the propagation of an acoustic wave in a random medium: e.g. the coherent backscattering effect recently observed for ultrasonic waves. We show that this effect arises as a consequence of reciprocity. Finally, in the fifth part, we discuss another property which is not taken into account in the radiative transfer theory: the reversibility of an acoustic wave propagating in a disordered medium.
MotsClés: Acoustic wave backscattering; Approximation theory; Diffusion; Mathematical models; Ultrasonic propagation; Coherent backscattering effects; Radiative transfer equation; Acoustic wave scattering


Transport parameters for an ultrasonic pulsed wave propagating in a multiple scattering medium. Tourin, A., A. Derode, A. Peyre, and M. Fink. Journal of the Acoustical Society of America 108, no. 2 (2000): 503–512.
Résumé: A set of ultrasonic experimental methods was developed to characterize a multiple scattering medium in terms of l(s), l*, l(a), respectively, the elastic, transport, and absorption mean free paths and D the diffusion constant. Actually, these quantities are the key parameters for a wave propagating in a disordered medium. Although they are widely used in optics, they are less common in acoustics. The underlying model is based on the expansion of the average solution for the heterogeneous Green's function equation. To validate this theoretical approach, a sample made of randomly located steel rods was used as a prototype. Through timeresolved measurements of the transmitted amplitude, the difference between the ballistic and the coherent wave is highlighted. In varying the sample thickness, l(s) is determined, the coherent and diffusive regime are distinguished, and the transition from one to the other is followed. Furthermore, as a limit to a description of the average intensity based on the diffusion approximation, the existence of a coherent backscattering effect is shown. This latter gives a method to estimate D and l*. These quantities being determined, it becomes possible to infer l(a) using average timeresolved intensity measurements. Finally, some applications to coarsegrain stainless steels are discussed. (C) 2000 Acoustical Society of America.
MotsClés: acoustics; article; calculation; mathematical analysis; priority journal; sound; theory; ultrasound


Limits of timereversal focusing through multiple scattering: Longrange correlation. Derode, A., A. Tourin, and M. Fink. Journal of the Acoustical Society of America 107, no. 6 (2000): 2987–2998.
Résumé: Experimental results of timereversal focusing in a highorder multiple scattering medium are presented and compared to theoretical predictions based on a statistical model. The medium consists of a random collection of parallel steel rods. An ultrasonic source (3.2 MHz) transmits a pulse that undergoes multiple scattering and is recorded on an array. The timereversed waves are sent by the array back to the source through the scattering medium. The quality of temporal focusing is very well predicted by a simple statistical model. However, for thicker samples, persistent temporal side lobes appear. We interpret these sidelobes as a consequence of the growing number of crossing paths in the sample due to highorder multiple scattering. As to spatial focusing, the resolution is practically independent from the array's aperture. With a 16element array, the resolution was found to be 30 times finer than in a homogeneous medium. Resolutions of the order of the wavelength (0.5 mm) were attained. These results are discussed in relation with the statistical properties of timereversal mirrors in a random medium. (C) 2000 Acoustical Society of America.
MotsClés: acoustics; article; priority journal; signal noise ratio; signal transduction; sound transmission; statistical analysis; thickness


Coherent Backscattering of an Elastic Wave in a Chaotic Cavity. De Rosny, J., A. Tourin, and M. Fink. Physical Review Letters 84, no. 8 (2000): 1693–1695.
Résumé: We report the first experimental evidence of coherent backscattering enhancement for transient elastic waves propagating in a twodimensional chaotic cavity. The timeintegrated squared amplitude at the point source is twice as large as at the other points around the source. Contrary to analogous optical experiments, this effect is already clearly observable on a single realization. Especially, the spatial shape of the coherent backscattering enhancement is well predicted by a generalization of the existing theory.


Dynamic time reversal of randomly backscattered acoustic waves. Tourin, A., A. Derode, and M. Fink. Europhysics Letters 47, no. 2 (1999): 175–181.
Résumé: We report the first experiments using the reversibility of a transient acoustic wave in a multiplescattering medium to simulate either a stationary or a dynamic acoustic lens. The method is based on time reversal experiments performed in a backscattering configuration. In the stationary case, we show that we take advantage of multiple scattering to focus better than with a perfect reflecting interface. In the dynamic case, we explain the refocused spot time evolution by a simple model based on the timedependent ability to recover the angular spectrum thanks to both single and multiplescattering paths.


Time reversal in multiply scattering media. Derode, A., A. Tourin, and M. Fink. Ultrasonics 36, no. 15 (1998): 443–447.
Résumé: The application of timereversal mirrors (TRM) to media with very highorder multiple scattering is presented. Random sets of up to 2500 steel rods are considered. When a pulsed wave traverses such a medium, it undergoes many scatterings before reaching the TRM. The resulting pressure field spreads in time, up to 300 times the initial pulse duration; it is recorded, timereversed and retransmitted through the same disordered medium. Surprisingly, the timereversed waves are found to converge to their source and recover their original waveform and duration, unlike one could have expected given the high order of multiple scattering involved and the usual sensitivity to initial conditions of timereversal processes. In addition to this, the observed resolution of the timereversed waves was greatly increased, and found to be smaller than the theoretical limit for the array's aperture. Theoretical limits of timereversed experiments are discussed. © 1998 Elsevier Science B.V.
MotsClés: Multiple scattering; Time reversal; Steel; Ultrasonic transmission; Ultrasonics; Time reversal mirrors (TRM); Ultrasonic scattering

